While working in the shipyards he joined the Unite and GMB trade unions, later joining PCS whilst at Scottish Enterprise.[20] He is also on the executive committee of the Scottish Fabian Society. Sweeney came to prominence during the 2014 Scottish independence referendum, after he organised an open letter signed by young shipyard workers opposing the break-up of the UK, and subsequently spoke at a rally alongside Gordon Brown on the eve of the referendum.[21][22][23][24]

Sweeney has an interest in built heritage and architectural issues in Glasgow.[32] He is a member of Glasgow Building Preservation Trust[33] and has led walks as part of Glasgow Doors Open Days Festival for several years.[34] Sweeney was also involved in the restoration of the historic former Govan shipyard head offices into the Fairfield Heritage Centre, for which he won an award.[35] After campaigning against the demolition of Springburn Public Halls in 2012,[36] he founded the Springburn Winter Gardens Trust, which is working to restore the nearby Springburn Winter Gardens.[37]